JEE Advanced Mathematics: Trigonometry Practice Questions

11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$If tan theta equals 1, what is the value of theta in the interval 0 to 90 degrees?$
Easy
Q2.
$What is the value of sec squared theta minus tan squared theta?$
Easy
Q3.
$Simplify the expression sin(180 degrees minus theta).$
Easy
Q4.
$If tan theta = 1/7 and sin phi = 1/sqrt(10), where theta and phi are acute angles, then find the value of theta + 2 phi.$
Medium
Q5.
$If cos alpha + cos beta + cos gamma = 0 and sin alpha + sin beta + sin gamma = 0, then find the value of cos(alpha - beta).$
Medium
Q6.
$Find the number of solutions of the equation sin x = x/10 in the interval (-pi, pi).$
Medium
Q7.
$Find the maximum value of the expression 3 sin x + 4 cos x + 5.$
Medium
Q8.
$I f a l p haan d b e t aa r er oo t so f t h ee q u a t i o n x^{2} - 2 x cos (t h e t a) + 1 = 0, f in d t h e v a l u eo f a l p h a^{n} + b e t a^{n} .$
Hard
Q9.
$Find the value of the infinite product cos(pi/4) * cos(pi/8) * cos(pi/16) * ... up to infinity.$
Hard
Q10.
$Solve for x in the interval [0, 2pi] for the equation sin(x) + sin(2x) + sin(3x) = 0.$
Hard
Q11.
$F in d t h e ma x im u m v a l u eo f t h e f u n c t i o n f (x) = s i n^{2} (x) + s i n^{2} (x + p i /3) + cos (x) cos (x + p i /3) .$
Hard

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